# Directions to Proxima Centauri

I'm writing a sci-fi novel in which humans venture to the stars for the first time. Their "shake down" cruise takes them to Proxima Centauri. I'm trying to understand where Proxima Centauri is located relative to the sun rather than Earth, as that seems a more logical reference for navigation to nearby stars.

The location of Proxima Centauri in Earth's night sky is described with the Earth-relevant coordinates

Right ascension 14h 39m 36.49400

Declination –60° 50′ 02.3737

However, the Earth's orbit is inclined 7.155° to the Sun's equator and our axis is tilted at 23.4392811°.

Is there a reference indicating Proxima Centauri's sol-relative position, or can that position be calculated based on the above information?

• You mean, it isn't Third Star to the Right and Straight on 'Til Morning? – Carl Witthoft Jun 25 '18 at 18:14

A system of coordinates requires a fixed plane to define "zero latitude" and a direction chosen in that plane to define "zero longitude".

For directions to the stars, the distances are so great that it matters not if you base your coordinates at the Sun or at the Earth, because the distance between the Sun and Earth is so small in relation to the distances to the stars.

There are a few coordinate systems in use. The first uses the Earth's Equator as the fixed plane and the direction of the sun on March 21 (vernal equinox) as the direction of zero longitude. For historical reasons the longitude in this system is called Right Ascension and latitude is called Declination. It would be quite suitable for your adventurers to use.

You can also use the plane of the solar system, or the plane of the galaxy as the fixed plane. In these coordinates systems Proxima is located at

-44:45:47.62 Latitude(deg)   +239:06:53.08 Longitude(deg) Ecliptic
-01:55:37.90 Latitude(deg)   +313:56:23.96 Longitude(deg) Galactic


But remember that Proxima is moving, so these figures are not fixed.

• That last part is important. Not only is PC not where we observe it (old photons and all) but it will have moved rather a lot during the flight time. – Carl Witthoft Jun 25 '18 at 18:15

Equatorial coordinates do refer to Earth's rotation and orbit, but the related International Celestial Reference System (ICRS) can also be used in deep space. The ICRS origin is the solar system barycenter, and the coordinate axes are aligned with the Earth equator and equinox as of the year 2000. The International Celestial Reference Frame (ICRF) is a catalog of precise ICRS positions of a few hundred extragalactic radio sources, mostly quasars. In optical wavelengths, a Hipparcos reference frame links stars in this galaxy to ICRS, and a Gaia reference frame of quasars is in development.

A complete star catalog includes not only equatorial positions at the reference epoch but also parallaxes and proper motions. Parallax, inversely related to distance, is the annual wobble of a star's geocentric position around the heliocentric average, less than 1 arcsecond even for the nearest stars. Proper motion is the change in apparent position over time as the Sun and other stars move around the galaxy. With this information plus radial velocity, the crew could predict and analyze the apparent positions of nearby stars as the spacecraft travels among them. The ICRF quasars' great distance fortunately makes their parallaxes and proper motions negligible but unfortunately makes them rather faint in the optical band.

In addition to on-board astrometry, I suppose the spacecraft would use star trackers for navigation. Satellites and planetary probes commonly track Canopus as it is very bright and fairly distant. Other distant bright stars such as Rigel or Deneb might help with attitude control. Nearby stars such as Sirius and Vega would appear to shift by a few degrees as the spacecraft progressed toward its destination. By the end of the trip, the Sun would fade to magnitude +0.4 but remain a useful reference point.

I think I have a better way for you to visualize locations of stars relative to the sun. I am also writing a science-fiction book/series so I would be glad to share ideas. I have finished one book of what I hope to one day be an eight book series. Over the course of my eight books, I am having a generation starship visit 18 star systems then return to Earth over a 600 year period. I wanted to visualize the shortest route so I actually built a 3D model out of foam balls and stiff wire. It takes about a half an hour to make this if you have the following information:

GALACTIC (CARTESIAN) COORDINATES

Create an X,Y,Z coordinate system with the following directions:

X,Y plane is the "galactic plane": this is not well defined, but ideally there is an equal amount of mass (or star count) above and below the plane

X: line pointing in the direction of the center of the galaxy from the sun (distance of sun "above" the plane is negligible compared to the distance to the galactic center/ we arbitrarily choose the sun to be "above" the galactic plane (about 67 +/- 11 Light Years according to Humphrey & Larsen 1995AJ Vol 110 p 2183)

Y: line perpendicular to X, positive in the direction of galactic rotation

Z: line perpendicular to the galactic plane that passes through the sun, positive in the "Galactic North" direction (farther "above" the galactic plane)

Now set the sun at (X,Y,Z) = (0,0,0).

Using these coordinates Proxima was at (2.946,-3.021,-0.169) in the year 2000 per: http://www.stellar-database.com/Scripts/search_star.exe?Name=alpha+centauri Of course stars move, but if your book is near future this is close enough.

This method would just be for visualization and you would probably need to put in a few more nearby stars to get relative locations. For navigation, answers above would work (if you used a computer to calculate where Proxima will be at arrival time, you point that way and make small corrections when you get close).

Check out this cool 3D plot: http://www.atlasoftheuniverse.com/50lys.html At this scale, Proxima and Alpha Centauri are in the same place.

• That's very cool. I actually started a project to visualize the nearest stars in a browser using WebGL, but it's a back-burner thing. Thought it would be a fun tool for my readers to visualize where the story takes place. If I find time to finish it up, I'm glad to share. If you want to connect about writing, my email address is in my Stackexchange profile. – Eric J. Jul 3 '18 at 19:09